Are you busy 'in' cooking is not correct. You could use 'with' instead, however connector words are not necessary for this sentence. I hope this helps.

Also a few other options 1) are you busy with your cooking? 2) are you busy doing cooking? 3) are you busy cooking? 4) are you busy and cooking? Probably a few more and as mentioned before the correct option is "are you busy with cooking" 😊

While this can be said using a preposition, "Are you busy cooking?" is correct in and of itself too :)

it's "are you busy with cooking. "